Аннотация:
В прикладных задачах часто возникает необходимость решать уравнение диффузии. Наиболее эффективными методами решения подобного рода задач являются сеточные методы, которые, тем не менее, обладают погрешностями аппроксимации. В данной работе рассмотрено линейное уравнение диффузии с переменными коэффициентами, для которого найдена оценка погрешности аппроксимации схемой с весами. Предложен алгоритм нахождения оптимального значения веса, обеспечивающего минимум погрешности для данного значения шага сетки.
Ключевые слова:
уравнение диффузии, схемы с весами, погрешность аппроксимации.
Образец цитирования:
А. И. Сухинов, А. Е. Чистяков, А. В. Шишеня, “Оценка погрешности решения уравнения диффузии на основе схем с весами”, Матем. моделирование, 25:11 (2013), 53–64; Math. Models Comput. Simul., 6:3 (2014), 324–331
V. V. Sidoryakina, “Existence and Uniqueness of the Initial-Boundary Value Problem Solution of Multicomponent Sediments Transport in Coastal Marine Systems”, CMIT, 7:2 (2023), 73
Vladimir Litvinov, Nelli Rudenko, Natalya Gracheva, Alexander Chistyakov, I. Malygina, “A software package for solving grid equations in areas with geometry “stretched” along one of the spatial directions”, E3S Web Conf., 363 (2022), 02021
А. И. Сухинов, Ю. В. Белова, А. Е. Чистяков, “Моделирование биогеохимических циклов в прибрежных системах Юга России”, Матем. моделирование, 33:3 (2021), 20–38; A. I. Sukhinov, Y. V. Belova, A. E. Chistyakov, “Mathematical modeling of biogeochemical cycles in coastal systems of the South of Russia”, Math. Models Comput. Simul., 13:6 (2021), 930–942
N D Panasenko, A Yu Poluyan, N S Motuz, “Algorithm for monitoring the plankton population dynamics based on satellite sensing data”, J. Phys.: Conf. Ser., 2131:3 (2021), 032052
Alexander I. Sukhinov, Alexander E. Chistyakov, Elena A. Protsenko, Valentina V. Sidoryakina, Sofya V. Protsenko, Communications in Computer and Information Science, 1263, Parallel Computational Technologies, 2020, 279
Sukhinov A.I. Chistyakov A.E. Protsenko S.V. Sidoryakina V.V., “Coupled 3D Wave and 2D Bottom Deposit Transportation Models For the Prediction of Harmful Phenomena in Coastal Zone”, Trends in the Analysis and Design of Marine Structures, Proceedings in Marine Technology and Ocean Engineering, 2, ed. Parunov J. Soares C., Crc Press-Balkema, 2019, 597–603
Sukhinov A.I. Chistyakov A.E. Sidoryakina V.V. Protsenko E.A., “Parallel Numerical Solution of the Suspension Transport Problem on the Basis of Explicit-Implicit Schemes”, Parallel Computational Technologies, Pct 2019, Communications in Computer and Information Science, 1063, ed. Sokolinsky L. Zymbler M., Springer International Publishing Ag, 2019, 256–268
Gushchin V.A. Sukhinov I. Chistyakov A.E. Sidoryakina V.V., “Optimal Value of Weight Parameter in the Scheme With Weights For the Diffusion-Convection Equation”, AIP Conference Proceedings, 2172, ed. Pasheva V. Popivanov N. Venkov G., Amer Inst Physics, 2019, 070014
Chistyakov Alexander, Elena Protsenko, SECOND INTERNATIONAL CONFERENCE ON MATERIAL SCIENCE, SMART STRUCTURES AND APPLICATIONS: ICMSS-2019, 2201, SECOND INTERNATIONAL CONFERENCE ON MATERIAL SCIENCE, SMART STRUCTURES AND APPLICATIONS: ICMSS-2019, 2019, 050020
Alexander Chistyakov, Elena Protsenko, Asya Atayan, SECOND INTERNATIONAL CONFERENCE ON MATERIAL SCIENCE, SMART STRUCTURES AND APPLICATIONS: ICMSS-2019, 2201, SECOND INTERNATIONAL CONFERENCE ON MATERIAL SCIENCE, SMART STRUCTURES AND APPLICATIONS: ICMSS-2019, 2019, 050040
Alexander I. Sukhinov, Alexander E. Chistyakov, Valentina V. Sidoryakina, Elena A. Protsenko, Communications in Computer and Information Science, 1129, Supercomputing, 2019, 39
Sofya Protsenko, SECOND INTERNATIONAL CONFERENCE ON MATERIAL SCIENCE, SMART STRUCTURES AND APPLICATIONS: ICMSS-2019, 2201, SECOND INTERNATIONAL CONFERENCE ON MATERIAL SCIENCE, SMART STRUCTURES AND APPLICATIONS: ICMSS-2019, 2019, 050037
Yulia Belova, Alena Filina, SECOND INTERNATIONAL CONFERENCE ON MATERIAL SCIENCE, SMART STRUCTURES AND APPLICATIONS: ICMSS-2019, 2201, SECOND INTERNATIONAL CONFERENCE ON MATERIAL SCIENCE, SMART STRUCTURES AND APPLICATIONS: ICMSS-2019, 2019, 050026
Valentina Sidoryakina, SECOND INTERNATIONAL CONFERENCE ON MATERIAL SCIENCE, SMART STRUCTURES AND APPLICATIONS: ICMSS-2019, 2201, SECOND INTERNATIONAL CONFERENCE ON MATERIAL SCIENCE, SMART STRUCTURES AND APPLICATIONS: ICMSS-2019, 2019, 050029
Alla Nikitina, Alena Filina, Yulia Belova, Tatiyana Lyashchenko, Vladimir Litvinov, Ludmila Kravchenko, Alla Zabalueva, SECOND INTERNATIONAL CONFERENCE ON MATERIAL SCIENCE, SMART STRUCTURES AND APPLICATIONS: ICMSS-2019, 2201, SECOND INTERNATIONAL CONFERENCE ON MATERIAL SCIENCE, SMART STRUCTURES AND APPLICATIONS: ICMSS-2019, 2019, 050025
Alexander I. Sukhinov, Alexander E. Chistyakov, Yulia V. Belova, H.-G. Gross, H. Khaled, T. Abbasian Najafabadi, D.A. Nguyen, I. Kudish, I.B. Sevostyanov, Y.G. Cen, K. Egiazarian, V. Mladenovic, G. Karapetyan, M. Minkin, “The difference scheme for the two-dimensional convection-diffusion problem for large peclet numbers”, MATEC Web Conf., 226 (2018), 04030
Alexander E. Chistyakov, Alla V. Nikitina, Elena A. Protsenko, H.-G. Gross, H. Khaled, T. Abbasian Najafabadi, D.A. Nguyen, I. Kudish, I.B. Sevostyanov, Y.G. Cen, K. Egiazarian, V. Mladenovic, G. Karapetyan, M. Minkin, “The distribution of pollutants in the ground layer of the atmosphere in the presence of forest plantations”, MATEC Web Conf., 226 (2018), 04029
А. И. Сухинов, А. Е. Чистяков, А. В. Шишеня, Е. Ф. Тимофеева, “Предсказательное моделирование прибрежных гидрофизических процессов на многопроцессорной системе с использованием явных схем”, Матем. моделирование, 30:3 (2018), 83–100; A. I. Sukhinov, A. E. Chistyakov, A. V. Shishenya, E. F. Timofeeva, “Predictive modelling of coastal hydrophysical processes in a multiprocession system based on explicit schemes”, Math. Models Comput. Simul., 10:5 (2018), 648–658
Alexander I. Sukhinov, Alexander E. Chistyakov, Alla V. Nikitina, Yulia V. Belova, Vladimir V. Sumbaev, Alena A. Semenyakina, Communications in Computer and Information Science, 910, Parallel Computational Technologies, 2018, 336
В. А. Гущин, А. В. Никитина, А. А. Семенякина, А. И. Сухинов, А. Е. Чистяков, “Модель транспорта и трансформации биогенных элементов в прибрежной системе и ее численная реализация”, Ж. вычисл. матем. и матем. физ., 58:8 (2018), 120–137; V. A. Gushchin, A. V. Nikitina, A. A. Semenyakina, A. I. Sukhinov, A. E. Chistyakov, “A model of transport and transformation of biogenic elements in the coastal system and its numerical implementation”, Comput. Math. Math. Phys., 58:8 (2018), 1316–1333